Schengen Help

Our plan at this point is to spend 90 days in Schengen then 90 days in the UK then 90 days back in Schengen then 90 days in USA then 90 days in Schengen.

Im unsure exactly how it works but i believe the UK and the USA have a similar 90/180 rules.

Also because the day i leave Schengen counts as both 'day 90' for the Schengen Visa and 'day 1' for the UK visa I believe that on day 179 i will be forced to leave the UK but wont yet be allowed back into Schengen??

Effectively both Visa's will say I need to stay out

Is there a way around this? Do i need to spend 1 day in a third country to break the cycle?

Also does my 90 day in, 90 day out, 90 day in, 90 day out, 90 day in, plan work or is there something else I'm missing stopping this from working??

UK and USA are not part of the Schengen area; therefore, any days you spend in the Schengen area do not count for your days in UK or USA. If you arrive to Schengen on day D and depart on day D+89, then arrive on day D+89+89, you satisfy the 90/180 rule.